a ladder 15 metres long just reaches the top of a vertical wall. if the ladder makes an angle of 60° with the wall, then the height of the wall will be
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Free solutions for Mathematics Exemplar Problems - class 10 Chapter 9 - Introduction to Trigonometry and Its Equations Introduction to Trigonometry and Its Equations - Exercise 8.3 question 4. These explanations are written by Lido teacher so that you easily understand even the most difficult concepts
NCERT Exemplar Solutions Class 10 Mathematics Solutions for Introduction to Trigonometry and Its Equations - Exercise 8.3 in Chapter 8 - Introduction to Trigonometry and Its Equations
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A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.
Answer:
Consider the vertical wall WL = x m (let)
Length of inclined ladder AW = 15 m ...[Given]
Ladder makes an angle of 60° with the wall.
\begin{array}{l} \therefore \frac{x}{15}=\cos 60^{\circ} \\ \Rightarrow \frac{x}{15}=\frac{1}{2} \\ \Rightarrow x=\frac{15}{2}=7.5 \end{array}
∴ 15 x =cos60 ∘ ⇒ 15 x = 2 1 ⇒x= 2 15 =7.5
Hence, the height of the wall = 7.5 m.
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A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60∘ with the wall, then find the height of the wall.
A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60∘ with the wall, then find the height of the wall.
Byju's Answer Standard X Mathematics Angle of Elevation A ladder 15 m... Question
A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of
60 ∘
with the wall, then find the height of the wall.
Open in App Solution
Given that, the height of the ladder = 15 m
Let the height of the vertical wall = h
And the ladder makes an angle of elevation
60 ∘ with the wall i.e., θ = 60 ∘ In Δ Q R P , cos 60 ∘ = P R P Q = h 15 ⇒ 1 2 = h 15 [ ∵ cos 60 ∘ = 1 2 ] ⇒ h = 15 2 = 7.5 m
Hence, the required height of the wall is
15 2 = 7.5 m . Suggest Corrections 41 Video Solution
EXEMP - Grade 10 - MATHEMATICS - Introduction to Trigonometry and its Applications - Q37
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Click here👆to get an answer to your question ✍️ A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60^∘ with the wall. Find the height of the wall.
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with the wall. Find the height of the wall.
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Updated on : 2022-09-05
Solution Verified by Toppr
Let the length of the ladder be =15m(hypotenuse)
The angle between the ladder and the wall ∠BCA=60
∘
Angle between ladder and the ground ∠CAB=90
∘ −60 ∘ =30 ∘
Height of the wall =BC
sin30 ∘ = 15 BC ⇒ 2 1 = 15 BC ⇒BC= 2 15 =7.5m
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